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The cost C of manufacturing a product can be estimated by the formula [#permalink]

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31 Jul 2011, 03:32

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A

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C

D

E

Difficulty:

55% (hard)

Question Stats:

63% (03:33) correct
37% (03:43) wrong based on 46 sessions

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The cost C of manufacturing a product can be estimated by the formula C= 0.03 rs t^2, where r ans s are amounts, in pounds, of two major ingredients and t is production time in hours. if r is increased by 50%, s increased by 20% and t decreased by 30%, by approximately what % will the estimated cost of manufacturing the product change.

A. 40% increase B. 12% increase C. 4% increase D. 12% decrease E. 24% decrease

Re: The cost C of manufacturing a product can be estimated by the formula [#permalink]

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31 Jul 2011, 06:15

tracyyahoo wrote:

The cost C of manufacturing a certain product can be estimated by the formular C=0.03rs(t^2), where r and s are the amounts, in pounds, oof the two major ingredients and t is the production time in hours. If r is increased by 50%, s is increased by 20%, and t is decreased by 30%, by approximately what percent will the estimated cost manufacturing the product change?

a) 40% increase b) 12% increase c) 4% incease d) 12% decease e) 24% decrease

pls explain me, thank you. I need it.

From the formula we deduce that C directly proportional to r, s and t^2 hence an increase or decrease in these values will directly change the value of C by that factor

There new r => 1.5r new s => 1.2s new t^2 = (0.7t)^2 = .49t^2 let the constant 0.03 be termed as A

Putting these new values: C1 = A*1.5r*1.2s*.49t^2 C1 = 0.882A*r*s*t^2 = 0.882(C)

Re: The cost C of manufacturing a product can be estimated by the formula [#permalink]

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31 Jul 2011, 15:19

Sudhanshuacharya wrote:

tracyyahoo wrote:

The cost C of manufacturing a certain product can be estimated by the formular C=0.03rs(t^2), where r and s are the amounts, in pounds, oof the two major ingredients and t is the production time in hours. If r is increased by 50%, s is increased by 20%, and t is decreased by 30%, by approximately what percent will the estimated cost manufacturing the product change?

a) 40% increase b) 12% increase c) 4% incease d) 12% decease e) 24% decrease

pls explain me, thank you. I need it.

From the formula we deduce that C directly proportional to r, s and t^2 hence an increase or decrease in these values will directly change the value of C by that factor

There new r => 1.5r new s => 1.2s new t^2 = (0.7t)^2 = .49t^2 let the constant 0.03 be termed as A

Putting these new values: C1 = A*1.5r*1.2s*.49t^2 C1 = 0.882A*r*s*t^2 = 0.882(C)

So new value = (1.5r)(1.2s)(.7r)^2=(15/10*12/10*49/100)(.03rst^2) Old value = (.03rst^2)

Now I am approx. 49 to 50 for faster calculation - New value = (15/10*12/10*50/100) = 180/100*1/2=(90/100)(.03rst^2)

New value is 90% of the old value So 10% less ....Let me see any value near 10% decreases B is the closest...So I go with B
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Re: The cost C of manufacturing a product can be estimated by the formula [#permalink]

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31 Jul 2011, 15:21

arjun007 wrote:

Hi

How did you guys determine if it was an increase or decrease?

is it because the value of c > c1?

Hope it is clear to you how it is decreasing ... Taking a larger value like - 50 even decreased,so obviously a smaller value - 49 will always decrease
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Re: The cost C of manufacturing a product can be estimated by the formula [#permalink]

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31 Jul 2011, 15:24

The reason for approximating is sometimes we make silly mistakes in calculation. So the best way is to pick smart numbers when needed.........Again it is up to you to decide the approach that works nest for you..... Some people can calculate this in head in (5-10) secs....then do not approximate...This is for the other folks who spend 20-30 secs on multiplication(calculation)
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Re: The cost C of manufacturing a product can be estimated by the formula [#permalink]

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31 Jul 2011, 19:14

tracyyahoo - Give kudos to jamifahad if you liked his approach...

That is one way of saying thanks for the person spending time on your questions.....
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The cost C of manufacturing a product can be estimated by [#permalink]

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05 Oct 2012, 08:03

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The cost C of manufacturing a product can be estimated by the formula C= 0.03 rs t^2, where r ans s are amounts, in pounds, of two major ingredients and t is production time in hours. if r is increased by 50%, s increased by 20% and t decreased by 30%, by approximately what % will the estimated cost of manufacturing the product change.

A. 40% increase B. 12% increase C. 4% increase D. 12% decrease E. 24% decrease
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Push+1 kudosbutton please, if you like my post

Last edited by Bunuel on 05 Oct 2012, 08:11, edited 1 time in total.

Re: The cost C of manufacturing a product can be estimated by the formula [#permalink]

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19 Dec 2014, 14:09

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